The role of a conserved threonine residue in the leader peptide of lasso peptide precursors

The conserved threonine (Thr) residue in the penultimate position of the leader peptide of lasso peptides microcin J25 and capistruin can be effectively replaced by several amino acids close in size and shape to Thr. These findings suggest a model for lasso peptide biosynthesis in which the Thr sidechain is a recognition element for the lasso peptide maturation machinery.     

Random sequential adsorption on fractals

Irreversible adsorption of spheres on flat collectors having dimension d < 2 is studied. Molecules are adsorbed on Sierpinski's triangle and carpet-like fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.     

Fe-N-C catalysts for oxygen electroreduction under external magnetic fields:Reduction of magnetic O2 to nonmagnetic H2O

An extensive analysis of iron-nitrogen-carbon(Fe-N-C)electrocatalysts synthesis and activity is presented concerning synthesis conditions such as initial Fe content,pyrolysis temperature and atmosphere(inert N₂,reducing NH₃,oxidizing Cl₂ and their sequential combinations)and the influence of an external magnetic field on their performance in oxygen reduction reaction(ORR).Thermosetting porous polymers doped with FeCl₃ were utilized as the Fe-N-C catalysts precursors.The pyrolysis temperature was varied within a 700-900℃range.The temperature and atmosphere of pyrolysis strongly affect the porosity and compositi on of the resultant Fe-N-C catalysts,while the in itial amount of Fe precursor shows much weaker impact.Pyrolysis under NH₃ yields materials similar to those pyrolyzed under an inert atmosphere(N₂).In contrast,pyrolysis under Cl₂ yields carbon of peculiar character with highly disordered structure and extensive microporosity.The application of a static external magnetic field strongly enhances the ORR process(herein studied in an alkaline environment)and the enhancement correlates with the Fe content in the Fe-N-C catalysts.The Fe-N-C materials containing ferromagnetic iron phase embedded in N-doped microporous carbon constitute attractive catalysts for magnetic field-aided anion exchange membrane fuel cell technology.     

Nonlocal elasticity in shape memory alloys modeled using peridynamics for solving dynamic problems

Nonlinear Dynamics - The work is primarily devoted to the peridynamic model elaborated for a solid body made of shape memory alloys (SMAs). The superelasticity effect is taken into consideration as...     

Neighbor Distinguishing Edge Colorings Via the Combinatorial Nullstellensatz Revisited

Consider a simple graph and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs.     

Boundary regularity of flows under perfect slip boundary conditions

We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ?-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.     

Weak relatively uniform convergences on MV-algebras

Weak relatively uniform convergences (wru-convergences, for short) in lattice ordered groups have been investigated in previous authors’ papers. In the present article, the analogous notion for MV-algebras is studied. The system s(A) of all wru-convergences on an MV-algebra A is considered; this system is partially ordered in a natural way. Assuming that the MV-algebra A is divisible, we prove that s(A) is a Brouwerian lattice and that there exists an isomorphism of s(A) into the system s(G) of all wru-convergences on the lattice ordered group G corresponding to the MV-algebra A. Under the assumption that the MV-algebra A is archimedean and divisible, we investigate atoms and dual atoms in the system s(A).     

<Emphasis Type=Italic>G</Emphasis>-compactness and groups

Lascar described E _KP as a composition of E _L and the topological closure of E _L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G _L . We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories. The first author is supported by the Polish Goverment grant N N201 384134. The second author is supported by the Polish Goverment grant N201 032 32/2231.     

Direct summands and retract mappings of generalized <Emphasis Type=Italic>MV</Emphasis>-algebras

In the present paper we deal with generalized MV-algebras (GMV-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, GMV-algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of GMV-algebras. The relations between GMV-algebras and lattice ordered groups are essential for this investigation. Supported by VEGA Agency grant 1/2002/05. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information, grant I/2/2005.